stanbul 2004
ne indepen-
is based on
ne indepen-
vation mod-
a particular
sonable de-
nation soft-
simple. We
proach
he class we
ed paradigm.
ious theory,
rk determi-
vare system
s: observa-
-olomina et
ing in time
(time epoch
ed observa-
vations, al-
pendent as
n principle,
' dependent
ze time de-
Yodels from
ation mod-
proach, the
h different
to internal
cover, with
ts and dis-
1 designed]
n more in-
nputational
the estima-
ftware im-
her words,
NA and an
m is possi-
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part Bl. Istanbul 2004
7.3 A unified exploitation approach
Unified theoretic frameworks lead to simple and efficient
algorithms and software. Unified software approaches lead
to simple and efficient exploitation procedures. In partic-
ular, an eventual software implementation of the concepts
presented, would lead to common shareable input/output
formats for a number of estimation engines.
A benefit of a unified approach is that we can follow dif-
ferent strategies and that we can combine them. In some
situations, one approach should be preferred. In other situ-
ations we can combine them. For a family of problems, one
approach may be preferred for calibration tasks whereas
the other may be preferred for orientation tasks.
Note, as mentioned in section 1, that the output estimated
parameters of a static network may be used as input obser-
vations for a time dependent network. Similarly, an SSA
engine can be used to generate initial approximations for a
NA engine. In all the cases, it is clear that interoperability
is easier to achieve with a unified approach.
8 CONCLUSION, ONGOING WORK AND
FURTHER RESEARCH
In this paper we have defined in a precise way the con-
cept of time dependent networks. The proposed concept
extends the classical unified (from geodesy, photogramme-
try and remote sensing) geomatic concept of network. In
short, a time dependent network is a classical network that
incorporates stochastic processes —that we call time de-
pendent parameters— and dynamic models —that we call
dynamic observation models. We have related time depen-
dent networks and their solution approaches to the exist-
ing Kalman filtering/smoothing and network methodolo-
gies —what we call the SSA and the NA solution appro-
aches— and have discussed their advantages and disadvan-
tages. Last, we have given some hints on how this unified
approach can be exploited at the software development and
data processing levels.
We are currently developing an experimental software pro-
totype that implements the concepts presented in this pa-
per. Further research will be related to the numerical so-
lution of SDEs for geomatic applications and to their op-
timization in terms of speed and memory/disk storage re-
quirements.
REFERENCES
Colomina, L, Navarro, J. and Térmens, A., 1992. Geo-
TeX: a general point determination system. In: Interna-
tional Archives of Photogrammetry and Remote Sensing,
Vol. 29-B3, International Society of Photogrammetry and
Remote Sensing, pp. 656—664.
FrieB, P., 1990. Kinematische Positionsbestimmung fiir die
Aerotriangulation mit dem NAVSTAR Global Positioning
System (Ph.D. Thesis). C, Vol. 359, Deutsche Geodätische
Kommission, München, DE.
183
Herring, T., 2003. GLOBK: Global Kalman filter VLBI
and GPS analysis program, version 10.1. Technical report,
MIT, Cambridge, MS, US.
Kalman, R., 1960. A new approach to linear filtering and
prediction problems. Transactions of the ASME, Journal
of Basic Engineering 82(1), pp. 3445.
Kloeden, P. and Platen, E., 1999. Numerical solution of
Stochastic Differential Equations. Springer Verlag, New
York, US.
Koch, K., 1995. Parameter estimation and hypothesis test-
ing in linear models. Springer Verlag, Berlin, DE.
Law ler, G., 1995. Introducttion to Stochastic Processes.
Chapman & Hall/CRC, Boca Ratón, FL, US.
Maybeck, P., 1979a. Stochastic models, estimation and
control. Mathematics in science and engineering, Vol. 141-
|, Academic Press Inc., New York, NY, US.
Maybeck, P., 1979b. Stochastic models, estimation and
control. Mathematics in science and engineering, Vol. 141-
2, Academic Press Inc., New York, NY, US.
Oksendal, B., 1993. Stochastic differential equations: an
introduction with applications. Universitext, third edn,
Springer-Verlag.
Scherzinger, B., 1997. A position and orientation post-
processing software package for inertial/GPS integration
(POSPROC). In: Proceedings of the KISS'97 Symposium,
Calgary, AB, CA, pp. 197-204.
Stoer, J. and Bulirsh, R., 1992. Introduction to Numerical
Analysis. second edn, Springer-Verlag, New York, US.
Térmens, A. and Colomina, L, 2003. Sobre la corrección
de errores sistemáticos en gravimetría aerotransportada,
(in Spanish). In: Proceedings of the 5. Geomatic Week,
Barcelona, ES.
Térmens, A. and Colomina, I., 2004. The Network Ap-
proach versus the State-Space Approach for strapdown in-
ertial kinematic gravimetry. Abstract submitted to the IAG
International Symposium Gravity, Geoid and Space Mis-
sions - GGSM2004, Porto, PT.
Teunissen, P., 2001. Dynamic data processing. Delft Uni-
versity Press, Delft, NL.
Xu, G., 2003. GPS theory, algorithms and applications.
Springer-Verlag, Berlin, DE.
ACKNOWLEDGEMENTS
The research reported in this paper has been performed
within the frame of the ITAVERA project that the Institute
of Geomatics is conducting for GeoNumerics and with par-
tial support of the Spanish Ministry of Science and Tech-
nology, through the OTEA-g project of the Spanish Na-
tional Space Research Programme (reference: ESP2002-
03687).